In a small bowl, whisk together the dairy-free milk and apple cider vinegar. Set aside to curdle for a few minutes.
In a large mixing bowl, whisk together the vegan butter, sugar, olive oil, vanilla extract, vegan yogurt, and the prepared vegan buttermilk.
Add the flour, baking powder, baking soda, and salt to the wet ingredients. Mix until just combined, being careful not to overmix.
Divide the batter into two equal portions. To one portion, add the cocoa powder and red food dye, mixing until smooth. Leave the other portion plain.
Line a loaf pan with parchment paper and grease it lightly with oil. Alternately spoon layers of the plain batter and red velvet batter into the pan. Use a knife to gently swirl the batters together to create a marble effect.
Preheat the oven to 350°F (175°C). Bake the loaf for 50-55 minutes, or until a toothpick inserted into the center comes out clean.
While the loaf is baking, whisk together the Violife cream cheese, powdered sugar, vanilla bean paste or extract, and a pinch of salt until smooth.
Allow the loaf to fully cool before spreading the frosting on top. Slice and enjoy!